# Percentage Difference,

Percentage Error,

Percentage Change

They are very similar ...

They all show a difference between two values as a percentage of one (or both) values

- Use Percentage Change when comparing an Old Value to a New Value
- Use Percentage Error when comparing an Approximate Value to an Exact Value
- Use Percentage Difference when both values mean the same kind of thing (one value is not obviously older or better than the other).

(Refer to those links for more details)

## How to Calculate

Step 1: Subtract one value from the other

Step 2: Then divide by ... what?

- Percentage Change: Divide by the
**Old Value** - Percentage Error: Divide by the
**Exact Value** - Percentage Difference: Divide by the
**Average**of The Two Values

Step 3: Is the answer negative?

- Percentage Change: a positive value is an increase, a negative value is a decrease.
- Percentage Error: ignore a minus sign (just leave it off), unless you want to know if the error is under or over the exact value
- Percentage Difference: ignore a minus sign, because neither value is more important, so being "above" or "below" does not make sense.

Step 4: Convert this into a percentage (multiply by 100 and add a % sign)

## The Formulas

*(Note: the "|" symbols mean absolute value, so negatives become positive.)*

Percent Change = \frac{New Value − Old Value}{|Old Value|} × 100%

### Example: There were 200 customers yesterday, and 240 today:

\frac{240 − 200}{|200|}× 100% = \frac{40}{200} × 100% = **20%**

A 20% increase.

Percent Error = \frac{|Approximate Value − Exact Value|}{|Exact Value|} × 100%

### Example: I thought 70 people would turn up to the concert, but in fact 80 did!

\frac{|70 − 80|}{|80|} × 100% = \frac{10}{80} × 100% = **12.5%**

I was in error by 12.5%

(Without using the absolute value, the error is **−12.5%**, meaning I under-estimated the value)

Percentage Difference = |\frac{First Value − Second Value}{(First Value + Second Value)/2}| × 100%

### Example: "Best Shoes" gets 200 customers, and "Cheap Shoes" gets 240 customers:

|\frac{240 − 200}{(200+240)/2}| × 100% = |\frac{40}{220}| × 100% = **18.18...%**

Rounded off, that is an 18% difference between them.